Το πανωφόρι μου είναι στην κρεμάστρα πίσω από την πόρτα.

In Greek, a possessed noun usually appears as article + noun + possessive word.

So:

το πανωφόρι μου = my coat

Literally, it looks a bit like the coat my / the coat of mine, but this is the normal Greek pattern. English usually does my coat, while Greek usually does the coat my.

Because μου is a weak possessive form, and in Greek it normally goes after the noun.

So:

• το πανωφόρι μου = my coat
• η πόρτα μου = my door
• το σπίτι μου = my house

This is one of the most basic word-order differences from English.

μου is the genitive weak personal pronoun of εγώ (I).

In this sentence, it functions like my:

• μου = my / of me

So although English uses a possessive adjective (my), Greek often uses this genitive clitic form after the noun.

πανωφόρι is neuter singular, so it takes the neuter singular definite article το.

That is why you get:

• το πανωφόρι = the coat

Gender in Greek is grammatical, so you have to learn each noun with its article:

• ο for masculine
• η for feminine
• το for neuter

Here, πανωφόρι happens to be neuter.

είναι is the present-tense form of to be used for he/she/it is and also they are.

Here the subject is το πανωφόρι μου (my coat), which is singular, so είναι means is:

• Το πανωφόρι μου είναι... = My coat is...

A common beginner confusion is with είμαι, which means I am.
So:

• είμαι = I am
• είναι = he/she/it is, they are

στην is a contraction of σε την.

• σε is a very common preposition that can mean in, on, at, or to, depending on context.
• την is the for a feminine singular noun in the accusative.

So:

• σε την κρεμάστρα → στην κρεμάστρα

In this sentence, English uses on:
στην κρεμάστρα = on the hanger

Greek often uses σε where English has different prepositions like in, on, or at.

It actually is in the accusative, because σε takes the accusative in Modern Greek.

The reason it looks unchanged is that many feminine nouns in -α have the same form in the nominative and accusative singular.

So:

• η κρεμάστρα = nominative, the hanger
• την κρεμάστρα = accusative, the hanger

The article changes clearly; the noun itself stays the same.

πίσω από is a set expression meaning behind.

So:

• πίσω από την πόρτα = behind the door

It is best to learn πίσω από as one unit.
If you translate word by word too literally, it can be confusing.

Yes, από often means from, but not always.

In the phrase πίσω από, it is part of the fixed expression behind. So here you should not translate από by itself as from.

Other similar expressions are:

• μπροστά από = in front of
• μακριά από = far from
• κοντά σε = near

So in this sentence, πίσω από simply means behind.

Because πόρτα is a feminine singular noun, and after από in this structure it appears in the accusative.

So:

• η πόρτα = nominative, the door
• την πόρτα = accusative, the door

This matches the prepositional phrase:

• πίσω από την πόρτα = behind the door

Because they give two layers of location.

• στην κρεμάστρα tells you where the coat is: on the hanger
• πίσω από την πόρτα tells you where that hanger is: behind the door

So the full idea is:

My coat is on the hanger, and that hanger is behind the door.

This stacking of location phrases is very natural in Greek.

Yes. Greek word order is more flexible than English word order.

The given sentence is a natural, neutral way to say it:

Το πανωφόρι μου είναι στην κρεμάστρα πίσω από την πόρτα.

You can move parts around for emphasis, especially location phrases, but the sentence may sound more marked or focused.

So for a learner, the original order is a very good model to follow.

The stress falls where the accent marks are:

• πανωφόρι = pa-no-FO-ri
• είναι = EE-ne
• κρεμάστρα = kre-MA-stra
• πίσω = PEE-so
• από = a-PO
• πόρτα = POR-ta

A rough full pronunciation guide is:

to pa-no-FO-ri mu EE-ne stin kre-MA-stra PEE-so a-PO tin POR-ta

πανωφόρι is a fairly general word for an outer garment, especially something like a coat or overcoat worn over other clothes.

In many everyday translations, coat is the simplest and most natural English choice.

So in this sentence, πανωφόρι is best understood as coat.